a) i. Let M and 4 be any two numbers the form 4r +1 of ii. Let mand N be any two numbers of the form 4r +3 Prove that in both cases (i) and (ii) the product 17.1 is of the form 47+1

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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a) i. Let M and I be any two numbers
N
of
the form 42+1
ii. Let 1 and N be any
M
of
the form 4r+3
Prave that in both cases (i) and (ii) the
product 1. 1 is of the form 47+1
시
6) Now Suppose that { P₁, P₂, P3,..., Pr} is a
finite collection of primes of the form
47 +3. Me introduce the number
N = 4( P₁ P₂ · P3 · · Px.) -1. Mimic the proof
of Euclid's I for Infinitude of Primes to show
that there are infinitely many primes of
the form 4r +3.
two numbers
Transcribed Image Text:a) i. Let M and I be any two numbers N of the form 42+1 ii. Let 1 and N be any M of the form 4r+3 Prave that in both cases (i) and (ii) the product 1. 1 is of the form 47+1 시 6) Now Suppose that { P₁, P₂, P3,..., Pr} is a finite collection of primes of the form 47 +3. Me introduce the number N = 4( P₁ P₂ · P3 · · Px.) -1. Mimic the proof of Euclid's I for Infinitude of Primes to show that there are infinitely many primes of the form 4r +3. two numbers
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